I am currently working on the problem joi16_skyscraper, which applies a connected-component DP technique. Although I have read several posts, I still do not understand how the DP works. Could someone explain the advantages of dividing problem into connected components and why the elements must be inserted in increasing order?

problem:

giving a grid of size 1e6*1e6 (in the beginning its all inf), we have 2 queries:

1 x y p: assign a[x][y]=p

2 x1 y1 x2 y2: print minimum element of subgrid start from (x1,y1) and end at (x2,y2)

I have some ideas like Dynamic 2D segment tree but I don't really sure thats work, can anyone suggests some other sol:>